Explaining divergence theorem and stoke-s theorem

Question

1) Write down physical significance of divergence of D?

2) State the divergence of a vector in three system of orthogonal Co-ordination.

3) What do you mean by divergence theorem?

4) Explain Stoke’s theorem in detail.

5) How is the unit vectors defined in three coordinate systems?

6) Electric field in a spherical co-ordinate is given by E = rρr/ 5ε. Demonstrate that closed ∫E.dS=∫(∇.E)Dv.

7)a) Define and prove divergence theorem.

b) What are the main sources of electromagnetic fields?

8) Check validity of divergence theorem taking into account the field D=2xy ax+x²ayc/m² and rectangular parallelepiped formed by planes x=0,x=1,y=0,y=2 &z=0,z=3.

9) A vector field D = [5r²/4]Ir is given in spherical co-ordinates. Estimate both sides of divergence theorem for volume enclosed between r=1 & r=2.

10) Given A= 2r cosΦ+Riφ in cylindrical co-ordinates for contour x=0 to 1, y= 0 to1, verify Stoke’s theorem.